First off, read the section on flagging in the help center - there's a ton of good information there, and links to more.
Second... Don't think too hard. Flagging is something that's made available to almost everyone who uses the site constructively even a little bit - as such, it generally doesn't rely on flaggers knowing a whole lot about how things work. Although you can spend the time to learn the deep and mysterious details of the system, you generally don't have to; flags always depend on someone or something else vetting your assertion that there's a problem, so if you make a mistake... It'll get caught before it does any real damage. Like everything else on these sites, flagging is powered by humans... So there will always be the potential for mistakes. But focus on raising flags where you're sure there's a real problem, and things should just work the vast majority of the time.
Finally... Looks like a lot of the confusion here arises from "link-only answers". A link-only answer is an answer that consists of zero relevant information beyond a link that may point at useful information elsewhere. Hence the word "only". Lots of folks get confused about this, which is why we don't use the term anywhere in the UI: what matters is whether or not the answer is... Well, an answer. If you see a link and you're unsure of what flag to use, chances are you're asking the wrong question... So ask yourself this:
- Is this answer impossible to understand? Very low quality.
- Can you understand the answer, but find it contains absolutely no information aimed at answering? Not an answer.
- Is there something else gravely wrong with the post (spam, abusive, plagiarism, etc.)? Use spam, abusive, or in need of moderator intervention flags.
- Is the post understandable and clearly attempting to answer, but simply wrong or poorly-written? Down vote.
In short, when you see a problem, focus on the problem and the proper flag will emerge. Don't work backwards trying to pound arbitrary posts into the shape of a flag, hoping a problem will emerge; don't use flags as "super-downvotes"; don't use a flag in lieu of an edit or a comment or an answer or anything other corrective action that you're empowered to perform yourself... And if you do any of these things then don't get all twisted up if whoever happens to respond to your flag doesn't do what you'd wish them to do.
###See also: Your answer is in another castle: when is an answer not an answer?